How do you solve the following system?: y=2x-3 , 2y=4x+3

Apr 1, 2018

$\text{no solution}$

Explanation:

$\text{consider the 2 equations expressed in "color(blue)"slope-intercept form}$

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$y = 2 x - 3 \to \left(1\right)$

$y = 2 x + \frac{3}{2} \to \left(2\right)$

$\text{both lines have } m = 2$

• " Parallel lines have equal slopes"

$\text{the 2 lines are therefore parallel and never intersect}$

$\Rightarrow \text{ there is no solution}$
graph{(y-2x+3)(y-2x-3/2)=0 [-10, 10, -5, 5]}